How to set up a simple FM patch like this?

I'm interested in learning the basics of simple FM synthesis. To start I'd like to recreate a simple patch which I think should show the principle well:

In this quick video, the guy uses:

1) A square wave two octaves above the note pitch
2) A saw wave at the note pitch
3) A square wave an octave below the note pitch

And gets a basic "growly" or edgy FM textured sound from it.

We have FM oscillators built into Reaktor. But I'm having trouble understanding how these things would be chained together to create something like this. I would really appreciate any pointers on how these would be linked up to recreate this simple patch.

The primary oscilators in reaktor don't use phase modulation , ( like your video )
For doing phase modulation is primary you use the ramp wave going into a ''sine'' math function . or you could use the core .phase modulation osc's
Scroll down to see my posted solutionhttps://www.native-instruments.com/forum/threads/self-oscillating-sine-fm.355339/
Just load up the factory ensemble FM4 , do know that the operators are sine waves only .
For getting a saw is just enough to feedback an operator by itself , for getting a square set modulattor to ratio 2 ( and a little bit of self feedback ) , and carrier to ratio 1 .
Also , ableton operator's operators , have lot's of partials to create user waves ,

Also the best advice I can give it so play with an fm synth , just enabling disabling operators and playin with their ratio while you have an osciloscope on you masterbus .

Here's a Blocks Rack that uses the same basic technique in terms of operator arrangement, waveforms (I think he uses band-limited waveforms for the modulators, you could emulate this by adding a LPF before the FM inputs), and ratios. I have also applied similar filtering and processing. Driver is quite different from the Vinyl Distortion (even though both combine filtering and non-linear processing), so this contributes to the different character of this patch. Let me know if you do not have Blocks Primes. I can substitute the CFG with Bento Box envelopes so you can still use it.

Note the LIN TZ setting on both of the Bento Box OSCs that are modulated. This is the closest you will get to DX7-style phase modulation (as in Operator) using our oscillators. It still sounds and behaves different, especially for waveforms other than sine. Same ballpark though. Try the FM amounts on the second and third oscillators to get different kinds of growls. Subtle changes have a strong effect here. If you turn up Feedback on the Monark Filter, you will get even more aggressive timbres.

Also note that phase alignment between the oscillators/operators does not work in the same way. I used sync from the unmodulated, lowest oscillator to the others in order to approximate the phase alignment found in a fixed synth like Operator. This type of sync has some quirks when using FM, but on the other hand you can create really interesting sounds by changing the Sync amounts on the oscillators.

Don't forget this is modular, so you can take this patch much further by applying more interesting modulation. Especially the processing using Driver and the Rounds Reverb is quite static now—adding envelopes, LFO, or sequencing to their parameters with add a lot of movement and texture. The same applies to the FM and Sync amounts on the oscillators.

sorry but the video doesn't show any FM- (better phase-) modulation. It is simple additive synthesis. The oscillators doesn't modulate any other oscillator's phase (or pitch).
It is a very simple patch you can get with any three-oscillators-synth. It is no typical FM-sound.

Phase-modulation depends typically on fix ratio between the frequencies of any oscillator.
It is important whether the oscillators have a fix starting point of phase (if wished).
Modulation from one oscillator's phase to other oscillator phase produces the typical sound.

sorry but the video doesn't show any FM- (better phase-) modulation. It is simple additive synthesis. The oscillators doesn't modulate any other oscillator's phase (or pitch).
It is a very simple patch you can get with any three-oscillators-synth. It is no typical FM-sound.

Click to expand...

This is not correct. The video indeed shows phase modulation using three operators. Operator A is modulated by operator B, which in turn is modulated by operator C. You can see this algorithm being selected in the bottom-right section.

sorry but the video doesn't show any FM- (better phase-) modulation. It is simple additive synthesis. The oscillators doesn't modulate any other oscillator's phase (or pitch).
It is a very simple patch you can get with any three-oscillators-synth. It is no typical FM-sound.

Phase-modulation depends typically on fix ratio between the frequencies of any oscillator.
It is important whether the oscillators have a fix starting point of phase (if wished).
Modulation from one oscillator's phase to other oscillator phase produces the typical sound.

Click to expand...

I didn't watch the video , just saw the screenshot of operator and assumed it was phase modulation .

This is not correct. The video indeed shows phase modulation using three operators. Operator A is modulated by operator B, which in turn is modulated by operator C. You can see this algorithm being selected in the bottom-right section.

Click to expand...

ah - ok thanks; very small
I supposed that the level knobs are only mixing knobs (additive). Didn't saw the matrix.
thanks for info

I looked through it. I'm trying to understand the basic principle behind what your synth and/or Ableton Operator is doing.

So is it correct that each operator from Ableton Operator is using a sine bank, as you did here? And when an operator is set to "saw" wave for example, it just adjusts the levels of the partials to reflect a saw wave for that operator?

If so, then how do the partials of one operator next modulate the partials of the next operator? Is each operator summed into a final output and that is then used out to modulate each partial of the next operator individually?

As a follow up to that question, more specifically, on a technical level, how does that modulation occur?

Would you just take the sum of operator 1's output, multiply it by a scaling factor for degree of impact, then add that output to the pitch (ie. 1-127) for the oscillator(s) of operator number 2?

ie. In a simple case, if you had one sine wave running at 440 hz with amplitude of 1 as your operator, and you multiplied its output by 12, then used that to modulate the 220 hz (pitch = 57) input of sine wave #2 (by adding its output to the pitch of sine #2), you would get sine #2 as a wave with a center frequency of 220 hz (pitch = 57), but changing in frequency between pitch 45 and 69 at a rate of 440 cycles per second?

Is that the basic principle? If not, how would it work? Thanks for any clarification.

I also see you guys talking about phase syncing of the oscillators. But as I can see it, phase syncing would only matter if they are running at exact multiples of one another, since they will desynchronize otherwise anyway. Or perhaps maybe you'd want them to resync every time you hit a note for a specific interaction I suppose.

Lastly what would be meant by phase modulation? What are you modulating then mathematically if not the oscillator frequency?

To illustrate, I tried putting together a simple model of how I think FM works (attached):

I think this is all correct, as it sounds okay. I note that using a frequency multiple of 0.5 adds one harmonic below the fundamental, and a frequency multiple of 0.25 adds two harmonics below the fundamental. Using a multiple of 2 adds harmonics only above the fundamental. I also note that if you increase magnitude too much the entire fundamental starts to shift, but at low values in remains in tune.

Is this all correct?

Thanks.

Attached Files:

I tried upgrading it to a three sine cascade (2 as cascaded modulators). Not sure if I did this right. All it did is give it some nice harmonic content so it sounds less sine-like. Is this still the right principle or am I not getting it? Is the harsh edge people get from FM in modern usage eg. in Ableton due to the effect across many partials simultaneously? Or am I missing something?

Attached Files:

sorry this is not correct. You are modulating the frequency of the oscillator which is FM-modulation used for broadcast.
Don't mistake it for digital FM in music application like YAMAHA's DX-serie. It is called FM too but it is really phase modulation (PM).
(mathematical background: FM modulates the phase too and FM and PM are cognate)
So use the core FM-oscillator (which must be correctly called PM-oscillator).
It doesn't modulate the frequency but the phase (input +ph):
When using multiple oscillators they are running free which means they sound different from time to time as they are running with different frequencies means they are out of phase (which is interesting musically too).
So they have to be reseted by a gate signal at input Rst. All oscillators start from same phase synchronously. Therefore you need the wrapper after the addition.

I didn't use the sine bank , but a true phase modulation oscillator in a core cell
I set reaktor to 10 voices , so there are actually 10 voices ( phase modulation osciillators ) , these are the partials that you see
The reaktor voice module info is verry important for this kind of stuff , the number of voices each have a unique I.D. nr 1,2,3,4,5etc..I used these to set the ratio ( multiply) of the individual voices
I controlled the output of each partial with a from voice module in combination with a mutlidisplay etccc...
The sine bank wouldn't work becasue it doesn't do phase modulation ,